Constraining cosmology and ionization history with combined 21 cm power spectrum and global signal measurements

Improvements in current instruments and the advent of next-generation instruments will soon push observational 21 cm cosmology into a new era, with high significance measurements of both the power spectrum and the mean ("global") signal of the 21 cm brightness temperature. In this paper we use the recently commenced Hydrogen Epoch of Reionization Array as a worked example to provide forecasts on astrophysical and cosmological parameter constraints. In doing so we improve upon previous forecasts in a number of ways. First, we provide updated forecasts using the latest best-fit cosmological parameters from the Planck satellite, exploring the impact of different Planck datasets on 21 cm experiments. We also show that despite the exquisite constraints that other probes have placed on cosmological parameters, the remaining uncertainties are still large enough to have a non-negligible impact on upcoming 21 cm data analyses. While this complicates high-precision constraints on reionization models, it provides an avenue for 21 cm reionization measurements to constrain cosmology. We additionally forecast HERA's ability to measure the ionization history using a combination of power spectrum measurements and semi-analytic simulations. Finally, we consider ways in which 21 cm global signal and power spectrum measurements can be combined, and propose a method by which power spectrum results can be used to train a compact parameterization of the global signal. This parameterization reduces the number of parameters needed to describe the global signal, increasing the likelihood of a high significance measurement.Comment: 16 pages, 8 figures. Revised to match accepted MNRAS version: expanded discussion of covariances between astrophysics and cosmology in Section 2.2, including two new figures; short discussion relating to KL modes added to Section 4; final results unchange

Redundant Array Configurations for 21 cm Cosmology

Realizing the potential of 21 cm tomography to statistically probe the intergalactic medium before and during the Epoch of Reionization requires large telescopes and precise control of systematics. Next-generation telescopes are now being designed and built to meet these challenges, drawing lessons from first-generation experiments that showed the benefits of densely packed, highly redundant arrays--in which the same mode on the sky is sampled by many antenna pairs--for achieving high sensitivity, precise calibration, and robust foreground mitigation. In this work, we focus on the Hydrogen Epoch of Reionization Array (HERA) as an interferometer with a dense, redundant core designed following these lessons to be optimized for 21 cm cosmology. We show how modestly supplementing or modifying a compact design like HERA's can still deliver high sensitivity while enhancing strategies for calibration and foreground mitigation. In particular, we compare the imaging capability of several array configurations, both instantaneously (to address instrumental and ionospheric effects) and with rotation synthesis (for foreground removal). We also examine the effects that configuration has on calibratability using instantaneous redundancy. We find that improved imaging with sub-aperture sampling via "off-grid" antennas and increased angular resolution via far-flung "outrigger" antennas is possible with a redundantly calibratable array configuration.Comment: 19 pages, 11 figures. Revised to match the accepted ApJ versio

INCIDENTAL AND JOINT CONSUMPTION IN RECREATION DEMAND

A theory for analyzing incidental consumption in a single site recreation demand model is presented. We show that incidental consumption on a recreation trip, such as a visit to see friends or a visit to a second recreation site, can be treated as a complementary good and analyzed using conventional theory. We also show that the analysis applies whether the side trips are incidental or joint. In a simple application we find that failing to account for incidental consumption appears to create little bias in valuing recreation sites.Resource /Energy Economics and Policy,

Effects of Antenna Beam Chromaticity on Redshifted 21~cm Power Spectrum and Implications for Hydrogen Epoch of Reionization Array

Unaccounted for systematics from foregrounds and instruments can severely limit the sensitivity of current experiments from detecting redshifted 21~cm signals from the Epoch of Reionization (EoR). Upcoming experiments are faced with a challenge to deliver more collecting area per antenna element without degrading the data with systematics. This paper and its companions show that dishes are viable for achieving this balance using the Hydrogen Epoch of Reionization Array (HERA) as an example. Here, we specifically identify spectral systematics associated with the antenna power pattern as a significant detriment to all EoR experiments which causes the already bright foreground power to leak well beyond ideal limits and contaminate the otherwise clean EoR signal modes. A primary source of this chromaticity is reflections in the antenna-feed assembly and between structures in neighboring antennas. Using precise foreground simulations taking wide-field effects into account, we provide a framework to set cosmologically-motivated design specifications on these reflections to prevent further EoR signal degradation. We show HERA will not be impeded by such spectral systematics and demonstrate that even in a conservative scenario that does not perform removal of foregrounds, HERA will detect EoR signal in line-of-sight $k$-modes, $k_\parallel \gtrsim 0.2\,h$~Mpc$^{-1}$, with high significance. All baselines in a 19-element HERA layout are capable of detecting EoR over a substantial observing window on the sky.Comment: 11 pages, 6 figures (10 total including subfigures), submitted to Ap

A Sensitivity and Array-Configuration Study for Measuring the Power Spectrum of 21cm Emission from Reionization

Telescopes aiming to measure 21cm emission from the Epoch of Reionization must toe a careful line, balancing the need for raw sensitivity against the stringent calibration requirements for removing bright foregrounds. It is unclear what the optimal design is for achieving both of these goals. Via a pedagogical derivation of an interferometer's response to the power spectrum of 21cm reionization fluctuations, we show that even under optimistic scenarios, first-generation arrays will yield low-SNR detections, and that different compact array configurations can substantially alter sensitivity. We explore the sensitivity gains of array configurations that yield high redundancy in the uv-plane -- configurations that have been largely ignored since the advent of self-calibration for high-dynamic-range imaging. We first introduce a mathematical framework to generate optimal minimum-redundancy configurations for imaging. We contrast the sensitivity of such configurations with high-redundancy configurations, finding that high-redundancy configurations can improve power-spectrum sensitivity by more than an order of magnitude. We explore how high-redundancy array configurations can be tuned to various angular scales, enabling array sensitivity to be directed away from regions of the uv-plane (such as the origin) where foregrounds are brighter and where instrumental systematics are more problematic. We demonstrate that a 132-antenna deployment of the Precision Array for Probing the Epoch of Reionization (PAPER) observing for 120 days in a high-redundancy configuration will, under ideal conditions, have the requisite sensitivity to detect the power spectrum of the 21cm signal from reionization at a 3\sigma level at k<0.25h Mpc^{-1} in a bin of \Delta ln k=1. We discuss the tradeoffs of low- versus high-redundancy configurations.Comment: 34 pages, 5 figures, 2 appendices. Version accepted to Ap

Calibration of Low-Frequency, Wide-Field Radio Interferometers Using Delay/Delay-Rate Filtering

We present a filtering technique that can be applied to individual baselines of wide-bandwidth, wide-field interferometric data to geometrically select regions on the celestial sphere that contain primary calibration sources. The technique relies on the Fourier transformation of wide-band frequency spectra from a given baseline to obtain one-dimensional "delay images", and then the transformation of a time-series of delay images to obtain two-dimensional "delay/delay-rate images." Source selection is possible in these images given appropriate combinations of baseline, bandwidth, integration time and source location. Strong and persistent radio frequency interference (RFI) limits the effectiveness of this source selection owing to the removal of data by RFI excision algorithms. A one-dimensional, complex CLEAN algorithm has been developed to compensate for RFI-excision effects. This approach allows CLEANed, source-isolated data to be used to isolate bandpass and primary beam gain functions. These techniques are applied to data from the Precision Array for Probing the Epoch of Reionization (PAPER) as a demonstration of their value in calibrating a new generation of low-frequency radio interferometers with wide relative bandwidths and large fields-of-view.Comment: 17 pages, 6 figures, 2009AJ....138..219

Emulating Simulations of Cosmic Dawn for 21cm Power Spectrum Constraints on Cosmology, Reionization, and X-ray Heating

Current and upcoming radio interferometric experiments are aiming to make a statistical characterization of the high-redshift 21cm fluctuation signal spanning the hydrogen reionization and X-ray heating epochs of the universe. However, connecting 21cm statistics to underlying physical parameters is complicated by the theoretical challenge of modeling the relevant physics at computational speeds quick enough to enable exploration of the high dimensional and weakly constrained parameter space. In this work, we use machine learning algorithms to build a fast emulator that mimics expensive simulations of the 21cm signal across a wide parameter space to high precision. We embed our emulator within a Markov-Chain Monte Carlo framework, enabling it to explore the posterior distribution over a large number of model parameters, including those that govern the Epoch of Reionization, the Epoch of X-ray Heating, and cosmology. As a worked example, we use our emulator to present an updated parameter constraint forecast for the Hydrogen Epoch of Reionization Array experiment, showing that its characterization of a fiducial 21cm power spectrum will considerably narrow the allowed parameter space of reionization and heating parameters, and could help strengthen Planck's constraints on $\sigma_8$. We provide both our generalized emulator code and its implementation specifically for 21cm parameter constraints as publicly available software.Comment: 22 pages, 9 figures; accepted to Ap